Regularization of Tunneling Rates with Quantum Chaos

TL;DR

This paper investigates how classical chaos influences quantum tunneling rates in double well potentials, showing that chaos tends to stabilize and narrow the range of tunneling splittings, leading to a more universal behavior.

Contribution

It demonstrates that classical chaos regularizes quantum tunneling rates, reducing their variability and producing a universal splitting-energy relation in chaotic systems.

Findings

Tunneling rates vary widely in regular wells but are narrowed in chaotic wells.

Chaos destabilizes periodic orbits, affecting tunneling rates.

The splitting vs. energy relation becomes more universal in chaotic systems.

Abstract

We study tunneling in various shaped, closed, two-dimensional, flat potential, double wells by calculating the energy splitting between symmetric and anti-symmetric state pairs. For shapes that have regular or nearly regular classical behavior (e.g. rectangular or circular) the tunneling rates vary greatly over wide ranges often by several orders of magnitude. However, for well shapes that admit more classically chaotic behavior (e.g. the stadium, the Sinai billiard) the range of tunneling rates narrows, often by orders of magnitude. This dramatic narrowing appears to come from destabilization of periodic orbits in the regular wells that produce the largest and smallest tunneling rates and causes the splitting vs. energy relation to take on a possibly universal shape. It is in this sense that we say the quantum chaos regularizes the tunneling rates.